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Effective theories for point sources

Nature comes to us with many hierarchies of scale, and science progresses because we do not need to understand them all at once. Effective theories exploit this fact to isolate what is important at any scale. This talk summarizes how effective theories work for applications to the ordinary and relativistic quantum mechanics of a particle moving within a potential, their role in singular “fall to the center” problems, and encoding how finite-size sources alter bound-state orbits.